# Multiple Kernel Clustering with Dual Noise Minimization

arXiv: https://arxiv.org/abs/2207.06041 · HTML: https://mlsanity.com/paper/2207.06041/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 64 references that are in the map.
- First posted on arXiv 13 Jul 2022.

## Builds on (most cited first, 13 of 13)

- [Deep Partial Multi-View Learning](https://mlsanity.com/paper/2011.06170/) (2020)
- [Large-scale Multi-view Subspace Clustering in Linear Time](https://mlsanity.com/paper/1911.09290/) (2019)
- [Simple Contrastive Graph Clustering](https://mlsanity.com/paper/2205.07865/) (2022)
- [Multi-VAE: Learning Disentangled View-common and View-peculiar Visual Representations for Multi-view Clustering](https://mlsanity.com/paper/2106.11232/) (2021)
- [Robust Graph Learning from Noisy Data](https://mlsanity.com/paper/1812.06673/) (2018)
- [Deep Density-based Image Clustering](https://mlsanity.com/paper/1812.04287/) (2018)
- [Align then Fusion: Generalized Large-scale Multi-view Clustering with Anchor Matching Correspondences](https://mlsanity.com/paper/2205.15075/) (2022)
- [Local Sample-weighted Multiple Kernel Clustering with Consensus Discriminative Graph](https://mlsanity.com/paper/2207.02846/) (2022)
- [Improved Dual Correlation Reduction Network](https://mlsanity.com/paper/2202.12533/) (2022)
- [Twin Learning for Similarity and Clustering: A Unified Kernel Approach](https://mlsanity.com/paper/1705.00678/) (2017)
- [Low-rank Kernel Learning for Graph-based Clustering](https://mlsanity.com/paper/1903.05962/) (2019)
- [A Convex Formulation for Spectral Shrunk Clustering](https://mlsanity.com/paper/1411.6308/) (2014)
- [Similarity Learning via Kernel Preserving Embedding](https://mlsanity.com/paper/1903.04235/) (2019)

## Built on by (most cited first, 10 of 10)

- [Hard Sample Aware Network for Contrastive Deep Graph Clustering](https://mlsanity.com/paper/2212.08665/) (2022)
- [Deep Incomplete Multi-view Clustering with Cross-view Partial Sample and Prototype Alignment](https://mlsanity.com/paper/2303.15689/) (2023)
- [A Survey of Deep Graph Clustering: Taxonomy, Challenge, Application, and Open Resource](https://mlsanity.com/paper/2211.12875/) (2022)
- [Auto-weighted Multi-view Clustering for Large-scale Data](https://mlsanity.com/paper/2303.01983/) (2023)
- [Reinforcement Graph Clustering with Unknown Cluster Number](https://mlsanity.com/paper/2308.06827/) (2023)
- [One-step Multi-view Clustering with Diverse Representation](https://mlsanity.com/paper/2306.05437/) (2023)
- [TMac: Temporal Multi-Modal Graph Learning for Acoustic Event Classification](https://mlsanity.com/paper/2309.11845/) (2023)
- [Scalable Incomplete Multi-View Clustering with Structure Alignment](https://mlsanity.com/paper/2308.16541/) (2023)
- [Efficient Multi-View Graph Clustering with Local and Global Structure Preservation](https://mlsanity.com/paper/2309.00024/) (2023)
- [MCFCN: Multi-View Clustering via a Fusion-Consensus Graph Convolutional Network](https://mlsanity.com/paper/2511.05554/) (2025)

## Abstract (arXiv)

Clustering is a representative unsupervised method widely applied in multi-modal and multi-view scenarios. Multiple kernel clustering (MKC) aims to group data by integrating complementary information from base kernels. As a representative, late fusion MKC first decomposes the kernels into orthogonal partition matrices, then learns a consensus one from them, achieving promising performance recently. However, these methods fail to consider the noise inside the partition matrix, preventing further improvement of clustering performance. We discover that the noise can be disassembled into separable dual parts, i.e. N-noise and C-noise (Null space noise and Column space noise). In this paper, we rigorously define dual noise and propose a novel parameter-free MKC algorithm by minimizing them. To solve the resultant optimization problem, we design an efficient two-step iterative strategy. To our best knowledge, it is the first time to investigate dual noise within the partition in the kernel space. We observe that dual noise will pollute the block diagonal structures and incur the degeneration of clustering performance, and C-noise exhibits stronger destruction than N-noise. Owing to our efficient mechanism to minimize dual noise, the proposed algorithm surpasses the recent methods by large margins.